This lesson covers the force vibration analysis of the Euler Bernoulli beam, a model widely used in various engineering applications. The lesson begins with a discussion on the general formulation of forced vibration problems and how they can be derived for the Euler Bernoulli beam. It then moves on to discuss the application of these formulations in different scenarios, using examples such as a bridge girder. The lesson also covers the principle of mode superposition, the concept of natural frequencies and mode shapes, and the use of Duhamel's integral in solving forced vibration problems. The lesson concludes with a detailed walkthrough of several examples, including the analysis of a simply supported beam subjected to harmonic excitation and a fixed-fixed beam subjected to uniformly distributed load.

- The Euler Bernoulli beam model is a useful tool in engineering applications.
- The principle of mode superposition is crucial in solving forced vibration problems.
- The concept of natural frequencies and mode shapes is essential in understanding the behavior of beams under different conditions.
- Duhamel's integral is a powerful tool in solving forced vibration problems.
- Understanding the application of these concepts in real-world scenarios, such as a bridge girder, can provide valuable insights.

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